\(\lim\left(\sqrt{2n^2+2n-1}-\sqrt{2n^2-n-5}\right)\) bằng
\(\dfrac{3\sqrt{2}}{4}\).\(\dfrac{3\sqrt{2}}{2}\).\(\dfrac{3\sqrt{2}}{5}\).\(\dfrac{3\sqrt{2}}{10}\).Hướng dẫn giải:\(\lim\left(\sqrt{2n^2+2n-1}-\sqrt{2n^2-n-5}\right)\)
\(=\lim\dfrac{3n+4}{\sqrt{2n^2+2n-1}+\sqrt{2n^2-n-5}}\)
\(=\lim\left(\left(3+\dfrac{4}{n}\right):\left(\sqrt{2+\dfrac{2}{n}-\dfrac{1}{n^2}}+\sqrt{2-\dfrac{1}{n}-\dfrac{5}{n^2}}\right)\right)\)
\(=\dfrac{3\sqrt{2}}{4}\)
